Hmmm - Somewhere I have an email from JW-Speaker who make the Daymakers. They highly recommend feeding from the battery via relays. With the JW-Speakers (esp the multi-voltage version) themselves it is possible for the units to show a low flicker effect at voltage less than 13V. I have seen this (and thus contacted Speaker) and it's also a problem on some cars with PWM lighting supplies.....
That is contradiction to their spec which as you see states operates an extremely wide voltage range, from 9V all the way to 32V.
(attached the 8700 7" spec - voltage range for 8630's are 10-32V)
So there is clearly a regulator in the system that caters to that, well below 'nominal 12V'
i.e. regardless of the voltage in, the regulator output voltage is constant (and the supplied voltage can even be quite low relative to what you might consider 'nominal' 12V)
With engine running, even without Relays, I would expect the voltage at the lamps to be comfortably higher than 13V for only 4A of load (low beam) for a pair of lamps (vs 10 for std incandescent lamps) with std wiring.
I too actually e-mailed them, to confirm my own deduction that there was no performance aspect associated with the supplied voltage and that confirmation was returned.
Unfortunately all my old email is wiped out, so don't have it quote specifically.
I have had multiple requests to supply relay kits for those with LED lamps - I could easily just take the money and supply what is asked, but that is not my modus operandi.
Disclaimer - I do not have these lamps, so my opinion is completely from my general knowledge of electronics, JwSpeaker published specs and JWS e-mail confirmation of my question.
If you say they flicker, then I have no reason to not believe you, but would be surprised that is from the voltage being too low.
Did the flicker occur with engine running or with just ignition-on?
I do note that JWS sells an "anti-flicker harness" - can't say for sure what that is exactly
http://www.jwspeaker.com/products/led-headlights-model-8700-evolution-2/8000381/
But appears to NOT be a relay system, but purely a "goes-into/goes-outa" device, (male H4 to female H4), presumably a filter to decouple low frequency noise.
It is conceivable that you might reduce noise picked up in the wiring harness by using a bypass wiring scheme (with relays) that is not laced into the main harness.